If we have a patient who has a severe latex allergy, why shouldn’t we just remove the stopper from the vial before withdrawing the vaccine in order to prevent a latex reaction?

It is not recommended to remove the stopper from a vaccine vial before administering a vaccine to a person who has a severe life-threatening allergy to latex. The vaccine has already been exposed to the rubber stopper in the vial, which might be enough of an exposure to cause a reaction. These people should not be given the vaccine.